Nuclear spin $3/2$ electric quadrupole relaxation as a quantum computation process

Abstract

In this work we applied a quantum circuit treatment to describe the nuclear spin relaxation. From the Redfield theory, we obtain a description of the quadrupolar relaxation as a computational process in a spin 3/2 system, through a model in which the environment is comprised by five qubits and three different quantum noise channels. The interaction between the environment and the spin 3/2 nuclei is described by a quantum circuit fully compatible with the Redfield theory of relaxation. Theoretical predictions are compared to experimental data, a short review of quantum channels and relaxation in NMR qubits is also present.

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

“…Another feature of equation (4.1) is that only the elements Dr 01 , Dr 02 , Dr 13 , Dr 23 depend on J 0 , showing that the Bell states are not affected by the phase damping channel [13]. The decoherence of the other elements is dictated by a GPD channel acting simultaneously on both qubits.…”

“…As detailed in Souza et al [13], the relaxation in this spin 3 2 system can alternatively be modelled by a quantum circuit treatment. In this treatment, the effect of the environment on the spin system is taken into account by considering the main system S as being composed of N subsystems that interact with the environment through quantum channels.…”

“…As a way to overcome these limitations, we proposed a QST method using only short non-selective RF pulses with a coherence selection scheme [10]. As a result, many studies involving quadrupolar nuclei could benefit from that method, including research on quadrupolar spin decoherence and relaxation [11][12][13][14] and quantum simulation [15]. Section 2 briefly expounds the main concepts regarding PPS and logic gate implementation and QST in high-field NMR of quadrupolar nuclei.…”

“…The idea of comparing the relaxation behaviour of two-qubit systems implemented by spin 1 2 and quadrupolar spin 3 2 nuclei is discussed in §4. To achieve that, we first describe the relaxation of quadrupolar spin 3 2 systems in terms of both the more NMR-friendly Redfield formalism [11,22] and quantum channels [13], more familiar in the QIP community [23,24]. Furthermore, the effect of the system-environment interaction on the behaviour of the classical and quantum correlation of spin 1 2 [25] and spin 3 2 [14] NMR systems is described, and the origin of the difference in behaviour is discussed.…”

On the quantumness of correlations in nuclear magnetic resonance

“…physical qubits. It is worth while to note that, during the decoherence dynamics, the amplitude-damping channel (which describes energy loss) acts individually on each qubit in both systems, while the phase-damping channel (responsible for coherence loss) is a global channel in case (i) and it acts independently over each qubit in case (ii) [18,33]. This difference allowed us to detect, in system (ii), a peculiar behaviour of the decoherence dynamics of quantum discord, i.e.…”